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Population with Continuous and Discrete Growth





User Instructions:


The simulator consists of three regions, the simulator's viewable window, the Growth model menu and the Simulation control menu.


The User Window:


The Growth Model Menu:



The values entered in both the Growth Model Menu are default values. User can change the values according to the Data to be tested (try to study the distributions with different values for the parameters).


• The Growth Model Menu contains two options, according to the population type that user is going to study. Choose the type of 'Population Growth Model' by clicking on the icon.



In the Growth Model Menu, the user can enter the values essential for running the simulator.


• The 'Time' (in Years) tab is where the user can enter the number of years that he/she wishes to study using the Simulator.



• The 'Number of steps' tab provides the user the option to run the simulator to as many steps he/she wishes it to run.



• The 'Initial population' number (N0) tab can be used to enter the starting or initial population number/count of the population being studied.


• For population with Discrete (in red) growth pattern:


The next two tabs include the:


'Number of births, B: tab is meant for entering the number of births.



'Number of deaths, D: tab is meant for entering the number of deaths.



The two above given tabs are the crucial ones to be filled in for Discrete population studies.


[Note: the minimum limit is 0. Negative values cannot be simulated]


• For population with Continuous (in blue) growth pattern:


'Rate of Growth' tab meant for entering the Rate at which the Study population is growing. [Note: the minimum limit is 0. Negative values cannot be simulated]



The above given tab is the crucial one to be filled in for Continuous population studies. 'B and D' are not considered in this simulation (refer theory).



From the next button onwards are the tools for 'Simulation Control':



• 'Go to step' button helps to make the simulator directly calculate thye population for the entered value for time in the same tab.



• 'Step run' button is meant for manually running the simulator, step by step. For example, if the population in every 0.1year is to be calculated, in each Step run, the population's possible change for every 0.1 year is calculated and produced.



• 'Run Iterations', as the literal word meaning runs the simulator slowly, step by step with the same previously entered values repeatedly till the T time. It can also be paused in between to get the values at the corresponding desired time.



• 'Play/pause' button as in all cases is for pausing (and continuing) the simulator at any step needed while performing Iterations (slowly, repeatedly calculating the population possible in each step).



• The 'Reset' button resets the simulator to the default values.



The 'Viewable Window' has some additional buttons meant for various other purposes,


• The 'Statistics' button is meant for viewing the time varying change in population step by step for the entered values in the simulator (for both types of Population).



A sample for the 'Viewable Window' when checking for the 'Statistics' could be,



Can be checked in case of both types the population.


• The next is the 'Data plots' button having a graph symbol, on clicking will change the 'Viewable Window' to a graphical plot.



A sample:



On moving the arrow key over the graph, the user can find the time and the exact population at the same time.


• The 'Work sheet' button is meant for mathematical calculation using equations (which the simulator would do automatically). On clicking the button the 'Viewable Window' will change to a window similar to a calculation board, where User can enter the required time in the 'At time' tab and simultaneously the population tab 'P' will get filled with the exact population value at time with respect to the studying population type.


For a Discrete population model,


Let for the time =2:



For continuous population:


For time =2:



If by mistake the user checks for the plot of a population when he/she had not 'Run Iterations' then the simulator automatically will show a new popup window that give alerts:



Step by Step explanation:


Step I:


Open the simulator and click the continuous growth option.



Step II:


Insert 100 in time T.



Step III:


Insert Ns as 10.



Step IV:


Insert No as 102.



Step V:


Insert R as 0.1012 from the data.



Step VI:


Click Run iterations option.



Step VII:


The simulator will start running a give the output depending on the input. According to the values inserted we see an increase in the Pac man characters (represents population). (Consider a Lion tailed monkey population.)



Step VIII:


After the population count is over, click data plots to get the graphical data.




From the graph it is clear that the given data shows growth according to the continuous growth model.

Step IX:


Click work sheet to check the data with math using the equation, Nt=N0ert



Note: Work sheet provided in the simulator will calculate the data using the formula, Nt=N0ert





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